The criticisms nonetheless did not end with Pearson. The English educational psychologist [1]} proposed a sampling model that generated the same correlation structure as a general factor model but that did not assume a single factor. In particular, whereas Spearman's model, and later extensions, proposed that positive correlations among P variables suggest the existence of one or more factors fewer than P, Thomson's sampling model assumed the opposite: that there are more factors than we have variables and that each variable is the result of a great number of independent causes, much greater than P. Even though it seems more plausible to assume that there are a great number of factors (mental subprocesses) that contribute to a score on any one ability test or item questionnaire, psychometricians following Spearman's footsteps ignored these criticisms and pursued a research program based on the indefensible premise that factor analysis and its extensions are statistical methods that can explain correlations in the observed data, rather than just describe them. It can be argued that the explanatory approach in which the existence of a hypothetical construct is inferred by performing exploratory analysis on limited sample self-report data cannot substitute the rigorous process of developing operational definitions of unobservable constructs on theoretical grounds or even on experimental measurements of the cognitive processes underlying the observed responses. Indeed, throughout the history of psychometrics, there have been repeated calls to guard against the reification fallacy in which a latent variable (e.g. mental ability) that captures a common variability in the data is treated as if it were a physical quantity (e.g. height) that is amenable to direct measurement [2]}, [3]}.
